[Numeracy 628] Re: That old thinking style thing

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Chip Burkitt chip.burkitt at orderingchaos.com
Fri Dec 17 18:36:48 EST 2010


I used to be an online mentor for the Drexel Math Forum
(http://mathforum.org/). One thing mentors had to do was provide
feedback not just about the accuracy of calculations or application of
algorithms. We encouraged students to fully describe their thought
process and over-explain their thinking. This often brought to light how
the students were understanding the problem. We did not interpret for
them but helped them with hints and suggestions. Students could continue
to submit responses as many times as they liked until they completely
understood what they were doing. Mentors scored responses on a three
point scale (Novice, Competent, Expert) in five different areas
(Clarity, Comprehension, Accuracy, Completeness, and Reflection). It's
been some years since I did this, so they may have changed things. But I
found their approach very useful in engaging students in basic math when
I was teaching students who had scored lowest on the mathematics
placement tests.

Chip Burkitt

On 12/17/2010 3:19 PM, Susan Jones wrote:

> It's the very last day of final exams.

>

> THis week I've been reminded with live in person people how important it is to learn *how to think* about the math as opposed to learning how to do the procedures. There are just too many procedures that kinda sorta look the same to keep track of them all. Not only that, this particular math curriculum makes problems that *don't* really look the same. I'm watching students who've avoided math all year struggle hard to memorize these procedures... so when the length is 6 more than the width, and you write "6w" and I ask "what math are you doing there?" you look blankly at me.

>

> I walk you through the "more than" concept and I watch it "click" and you are mildly astonished and think I'm wonderful... but I am thinking that it's time I at *least* put together some videos that take all that stuff with the x's and show LOTS of examples of putting numbers in there for the x's. For students who do have some number sense, plugging in numbers and *testing* adding 3x + 2x and discovering that it's 5x no matter what you call x... as long as you call it the same thing... could really help. (I'm also trying to figure out ways to do this that *aren't* entirely depending on language and discussion... some of my guys get *so* much smarter when they can see things...)

>

> I also stumbled over an article online about using videos to create a conceptual concept for fractions (full text is at http://springerlink.com/content/07300u8h0w40uj70/ ) -- and was mildly astonished myself that the researchers noted that the students did do better with the fractions, but that without direct intervention, focused on procedure, not concept. Yup, we can deliver the bestest and brightestest "conceptual framework" -- but to some of our students this is a bafflingly confusing way of showing them the procedures they're tuned in for. I've watched students read through "Six step problem solving methods" and the like and ... it's another Layer of Procedure. Not only do they have to figure out how to do the math, but they also have to figure out how to Do the Steps.

>

> I'm curious -- what are other folks doing to engage students in that elusive comprehension aspect?

>

> Susan Jones

> Academic Development Specialist

> Center for Academic Success

> Parkland College

> Champaign, IL 61821

> 217-353-2056

> sujones at parkland.edu

> Webmastress,

> http://www.resourceroom.net

> http://www.bicycleuc.wordpress.com

>

>

>

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